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The only all-Super League tie of the fourth round gives the Wolves the opportunity to avenge their shock 40-36 defeat in last year's quarter-finals at Craven Park.
The upset triggered a run of five successive defeats and created a depression at the Halliwell Jones Stadium.
"It derailed us psychologically for a while because we were simply kicked to pieces from all quarters," recalled Cullen.
"We were never allowed to forget it, which is not a healthy situation. At some point you've got to be allowed to put it behind you and move on. It caused us an awful lot of damage.
"It also came in the midst of a major injury crisis which got worse and it took us a while to get out of the hole that we had got ourselves into.
"But we've learned from it. As a group, when things don't quite go our way, we don't panic. We realise that what goes around, comes around. You've just got to hold your nerve and come through it."
The tie will take place on Saturday March 31, and be shown on BBC television with a 2.30pm kick-off.
The other televised tie will be at the Halton Stadium, where Widnes, once the Cup kings of rugby league, take on Wigan on Sunday April 1, with a 2.45pm start.
Both last year's finalists were handed home ties against National League opposition.
Holders St Helens, who have been made 7-4 favourites with William Hill, meet Batley in a repeat of the first-ever final of 1897 while Huddersfield take on York, whom they beat on their way to Twickenham last year.
The two remaining French clubs, Pia and Catalans Dragons, also landed home ties, against Harlequins and Featherstone respectively.
Leeds are 7-2 second favourites after landing a home tie against Workington.
Pia (France Elite) v Harlequins (SL), Keighley (NL2) v Oldham (NL2), Catalans Dragons (SL) v Featherstone (NL2), Bradford (SL) v Castleford (NL1), Dewsbury (NL1) v Sheffield Eagles (NL1), Whitehaven (NL1) v Halifax (NL1), Widnes (NL1) v Wigan (SL), Swinton (NL2) v Barrow (NL2), Leeds (SL) v Workington (NL2), London Skolars (NL2) v Wakefield (SL), St Helens (SL) v Batley (NL1), Rochdale (NL1) v Celtic Crusaders (NL2), Huddersfield (SL) v York (NL2), Warrington (SL) v Hull KR (SL), Gateshead (NL2) v Salford (SL), Hunslet (NL2) v Hull (SL).